Aw: [PEIRCE-L] The Proper Way in Logic (was Peirce's Ongoing Semiotic Project)

[Helmut Raulien]

Jon, List,

 

ontologically, in reality, a continuum cannot be built up from infinitesimally small points. But infenitesimality can only be infinitely  iterated towards in reality, if there already is a real continuum. So I see a tautology. Just imagine, that there would not be a real continuum: Then we nevertheless could get the idea of a continuum out of a line, which in reality consists of aligned, in this case not infinitesimally small points. Now we might say: If we are able to have the idea of a continuum, then there must be one. This argument is similar with Anselm´s proof of God. Ok, our world may be pixeled or quantized, but God´s realm is continuous. My Ockham´s-razor-argument in my last post neither is a proof for a real continuum, and whether Anselm´s proof is a proof, I don´t know. I sense platonism in the idea, that we cannot get an idea of something that does not exist. I am not totally convinced anymore about the reality of continuum. The question seems quasi-theological to me. 

 

Best, Helmut

 
 

Gesendet: Montag, 12. Februar 2024 um 20:57 Uhr
Von: "Jon Alan Schmidt" 
An: "Peirce-L" 
Betreff: Re: [PEIRCE-L] The Proper Way in Logic (was Peirce's Ongoing Semiotic Project)



Helmut, List:
 

According to Peirce, "Continuity represents 3ns almost to perfection" (CP 1.337, c. 1882). When we prescind discreteness from continuity, we are prescinding 2ns from 3ns, and we cannot prescind continuity from discreteness because we cannot prescind 3ns from 2ns. Since prescission "consists in supposing a state of things in which one element is present without the other, the one being logically possible without the other" (EP 2:270, 1903), the upshot is that 2ns is logically possible without 3ns, but 3ns is not logically possible without 2ns. Put another way, 3ns always involves 2ns as well as 1ns, and 2ns always involves 1ns. Nevertheless, 2ns cannot be built up from 1ns, and 3ns cannot be built up from 1ns and/or 2ns.

 

For example, a continuous line involves any discrete points within it, but it cannot be built up from any multitude of such points. The continuous whole (line) is ontologically prior to any discrete parts (points), which are indefinite (infinitesimal "linelets") unless and until they are deliberately marked off within it. Likewise, as I said before, the entire universe is an inexhaustible continuum (3ns) of indefinite possibilities (1ns), some of which are actualized (2ns). In Peirce's words, "The whole universe of true and real possibilities forms a continuum, upon which this Universe of Actual Existence is, by virtue of the essential 2ns of Existence, a discontinuous mark--like a line figure drawn on the area of the blackboard" (NEM 4:345, 1898; see also CP 6.203-209, 1898).



 

Regards,

 





Jon Alan Schmidt - Olathe, Kansas, USA

Structural Engineer, Synechist Philosopher, Lutheran Christian

www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt







 


On Mon, Feb 12, 2024 at 11:01 AM Helmut Raulien  wrote:




 


List, I think, we can prescind discreteness from continuity, e.g. by supposing the formation of attractors, or coagulation, or reentry (logical or actual loops), but we cannot prescind continuity from discreteness. So everything including thirdness is at first based on continuity, even if it requires discreteness. I think, that thirdness requires discreteness, because a relation as part of structure, and a habit too, can and has to be prescinded (or discriminated, or dissociated) as something discrete from continuity, to logically handle it.

 

Best, Helmut






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Re: [PEIRCE-L] The Proper Way in Logic (was Peirce's Ongoing Semiotic Project)

[Jon Alan Schmidt]

Helmut, List:

According to Peirce, we discover (not invent) continuity in
phaneroscopy--our conception of it comes from directly observing the flow
of time, which he calls "the continuum *par excellence*, through the
spectacles of which we envisage every other continuum" (CP 6.86, 1898), so
that "to say it is continuous is just like saying that the atomic weight of
oxygen is 16, meaning that that shall be the standard for all other atomic
weights. The one asserts no more of Time than the other asserts concerning
the atomic weight of oxygen; that is, just nothing at all" (CP 4.642,
1908). Here are a few more quotations about this.

CSP: To imagine time, time is required. Hence, if we do not directly
perceive the flow of time, we cannot imagine time. Yet the sense of time is
something forced upon common-sense. So that, if common-sense denies that
the flow [of] time is directly perceived, it is hopelessly entangled in
contradictions and cannot be identified with any distinct and intelligible
conception. But to me it seems clear that our natural common-sense belief
is that the flow of time is directly perceived. (NEM 3:60, c. 1895)

CSP: That this element [continuity] is found in experience is shown by the
fact that all experience involves time. Now the flow of time is conceived
as continuous. No matter whether this continuity is a datum of sense, or a
quasi-hypothesis imported by the mind into experience, or even an illusion;
in any case it remains a direct experience. (CP 7.535, 1899)

CSP: One opinion which has been put forward and which seems, at any rate,
to be tenable and to harmonize with the modern logico-mathematical
conceptions, is that our image of the flow of events receives, in a
strictly continuous time, strictly continual accessions on the side of the
future, while fading in a gradual manner on the side of the past, and that
thus the absolutely immediate present is gradually transformed by an
immediately given change into a continuum of the reality of which we are
thus assured. The argument is that in this way, and apparently in this way
only, our having the idea of a true continuum can be accounted for. (CP
8.123n, c. 1902)


Although Peirce acknowledges in the second passage that our direct
perception/experience of time might be an illusion, he nevertheless
suggests in the other two that its inescapability assures us of its
reality, and that this is the only way to account for our having the idea
of a true continuum at all. Moreover, right before the statement that I
quoted at the end of my last post, he makes the case at greater length that
we could not even imagine true continuity unless there were *something *in
reality that corresponds to it.

CSP: I will submit for your consideration the following metaphysical
principle which is of the nature of a retroduction: Whatever unanalyzable
element *sui generis* seems to be in nature, although it be not really
where it seems to be, yet must really be [in] nature somewhere, since
nothing else could have produced even the false appearance of such an
element *sui generis*. ...
In the same way, the very fact that there seems to be 3ns in the world,
even though it be not where it seems to be, proves that real 3ns there must
somewhere be. If the continuity of our inward and outward sense be not
real, still it proves that continuity there really is, for how else should
sense have the power of creating it?
Some people say that the sense of time is not in truth continuous, that we
only imagine it to be so. If that be so, it strengthens my argument
immensely. For how should the mind of every rustic and of every brute find
it simpler to imagine time as continuous, in the very teeth of the
appearances,--to connect it with by far the most difficult of all the
conceptions which philosophers have ever thought out,--unless there were
something in their real being which endowed such an idea with a simplicity
which is certainly in the utmost contrast to its character in itself. But
this something must be something in some sense like continuity. Now nothing
can be like an element so peculiar except that very same element itself. ...
The extraordinary disposition of the human mind to think of everything
under the difficult and almost incomprehensible form of a continuum can
only be explained by supposing that each one of us is in his own real
nature a continuum. (NEM 4:344-345, 1898)


Regards,

Jon

On Tue, Feb 13, 2024 at 9:18 AM Helmut Raulien  wrote:

> Jon, List,
>
> ontologically, in reality, a continuum cannot be built up from
> infinitesimally small points. But infenitesimality can only be infinitely
> iterated towards in reality, if there already is a real continuum. So I see
> a tautology. Just imagine, that there would not be a real continuum: Then
> we nevertheless could get the idea of a continuum out of a line, which in
> reality consists of aligned, in this case not infinitesimally small points.
> Now we might say: If we are able to have the idea of 

Re: [PEIRCE-L] Entropy and the Universal Categories (was Re: The Proper Way in Logic)

[John F Sowa]

Mike,

I realize that Peirce mentioned "crystals and bees" in the same sentence.  But 
we have to consider his classification of the sciences.  Pure mathematics comes 
first, and it does not depend on anything else.  It incudes all varieties, 
including formal or mathematical logic, discrete math, and continuous math.  
And Peirce followed Aristotle in insisting that continuous spaces (of which a 
line is a 1-D space) do not have points as parts.  For Aristotle and Peirce, 
points are markers that designate a locus ON a space, but are not parts OF the 
space.

That is the basis for Aristotle's solution to Zeno's paradox about Achilles and 
the turtle, which Peirce knew very well.

Phaneroscopy depends only on mathematics, not semeiotic.  For Peirce, the 
phaneron is raw, unprocessed and uninterpreted experience.  (Modern cognitive 
science has more to say about these issues, but it may be deferred for 
analyzing what Peirce wrote.)  The result of analyzing the phaneron is 
expressed in linguistic terms, which depend on psychic science, which may 
employ the methods of any and every science that precedes it.  That includes 
all previous sciences, including the physical sciences and other psychic 
sciences.

MB> I categorically disagree. Intentionality may be an example of Thirdness, 
but is not definitive of it.

I agree that Peirce did not define 3ns in terms of intentionality.  But every 
example that he cited does indeed involve intentionality.  Can anybody find a 
single example of Thirdness in any writings by Peirce that does not involve 
intentions at least at the level of a bacterium swimming upstream in a glucose 
gradient.  Even a description of how plants grow would involve Thirdness in the 
same sense as a bacterium.

But a description of a crystal could be stated in two ways.  If you consider 
the structure of the crystal as the desired final state, then a description in 
those terms would be stated in TERMINOLOGICAL thirdness.  That may be the 
reason why Peirce wrote "crystals and bees".   And that answer involves 
something very close to intentionality:  In forming a diamond, each atom of 
carbon goes to a position where it minimizes the total energy of the crystal 
structure.  In effect, the carbon atom "wants" to minimize energy in the same 
sense that a bacterium wants to ingest glucose.

But if you look at the way crystals actually grow in nature, each atom or 
molecule in the crystal goes into its spot in the structure by principles of 
2-ness -- following the strongest forces that act upon it.  Those are EXTERNAL 
forces that act upon the atoms.  That is very different from the INTERNAL 
forces in the bacterium that govern how it behaves in the presence of an 
external glucose gradient.

Take for example the two most common carbon crystals:  graphite and diamond.  
At modest level of heat, such as burning wood or paper, any unburnt carbon 
forms soot.  If you examine that soot with a powerful microscope, you'll find 
that the soot particles contain very small graphite crystals mixed with other 
residues of burning.  That can be explained by the atoms clumping together in a 
low energy state by 2ns, not 3ns,

But if you put the graphite under high compression at high temperatures, you 
can force the carbon atoms even closer together in a state with lower energy:  
diamond crystals.   Those are also external forces that act upon the carbon 
atoms.

Peirce knew the chemistry of his day very well.  But the atomic hypothesis of 
his day and theories about crystal formation were in their infancy.  With 
modern theories, descriptions at the level of 2ns can explain chemical 
reactions and the way atoms move in forming crystals.

John


From: "Mike Bergman" 
Sent: 2/12/24 5:19 PM

Hi John,
I categorically disagree. Intentionality may be an example of Thirdness, but is 
not definitive of it. JAS just posted "Continuity represents 3ns almost to 
perfection" (CP 1.337, c. 1882), which I concur best captures (with Mind) 
Peirce's prominent view of Thirdness, and contintuity does not require 
intentionality. You might even diagram it out.
And don't forget crystals (and atoms).
Best, Mike
On 2/12/2024 3:59 PM, John F Sowa wrote:
Mike,

In every example and application that Peirce wrote or cited, Thirdness involves 
intentionality.  But intentionality is not an anthropomorphic notion, it is 
biomorphic in the most fundamental sense.

Lynn Margulis wrote that a bacterium swimming upstream in a glucose gradient is 
a primitive example of intentionality, and no non-living physical system shows 
any kind of intentionality,  I believe that Peirce would agree, since he cited 
dogs, parrots, bees, and even plants at various times.

And by the way, viruses don't have intentions, since they're not alive.   They 
are signs that are interpreted by living things to produce more signs of the 
same kind.

John


From: "Mike Bergman" 

H

Re: [PEIRCE-L] Entropy and the Universal Categories (was Re: The Proper Way in Logic)

[John F Sowa]

Edwina,

Please see my response to Mike.

I used the word 'intentionality' because it (or something like it) is involved 
in all human actions.  For example, I can intentionally walk to the store.  But 
what about each step in the walk?  In effect, it is intentional, but it's only 
conscious when there is a puddle or a broken place in the sidewalk.

Other animals at every level and even plants act upon principles that would be 
called intentional if they had been human.  But consciousness is not necessary. 
 And even for humans, all actions appear to have the some kind of 
intentionality, but the actors themselves will often say that they did it 
"absent mindedly".

But absent minded actions are often done when people are "multitasking", such 
as talking on their cell phones while crossing the street and getting run over 
by a bus.  They didn't intend to get run over by the bus, but they did intend 
to cross the street.  The steps of walking were not conscious, but they were 
necessary parts of an intentional process.

In effect, Thirdness is involved in every intentional action.  And every 
instance of Thirdness by any living being could be called intentional if a 
human did it.   Can anybody find an example of Thirdness in any of Peirce's 
writings that could not be considered intentional if it had been performed by a 
human?

John


From: "Edwina Taborsky" 

List

I agree with Mike. Thirdness, in my view, does not imply or require 
intentionality. That, after all, suggests some kind of consciousness - and I 
think we find Thirdness in chemical and physical matter - and these forms of 
matter do not include consciousness.

I have a problem with the quote of “Continuity presents 3ns almost to 
perfection’ 1.337. I think that the rules of Thirdness CAN and must be, for a 
certain period of time, ‘continuous and stable.After all- we cannot live iin a 
world where a cat suddenly transforms into a dog.  BUT, since thirdness also 
includes 2ns and 1ns, then, it contains within itself, the ability to interact 
with other units of matter - as well as chance - and thus, has the capacity to 
accept more data and thus, change these ‘continuous rules’ and so, adapt and 
evolve.

Again - I consider that Peircean ‘continuity’ is not 3ns but is the continuous 
morphological semiosis formation of energy-into-matter - which is ongoing [ or 
else, as has been pointed out, entropy sneaks in]….

Edwina
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Aw: [PEIRCE-L] The Proper Way in Logic (was Peirce's Ongoing Semiotic Project)

[Helmut Raulien]

Jon, List,

 

the arguments in your Peirce-quotes are Ockham´s razor plus an analogy to Anselm´s proof of God. Both figures are not by everybody agreed to being valid. But I believe in continuum, I guess. I think, physicists donot quibble, whether the continuous fields- and waves- theory is the better one, or the discontinuous quantums-theory, but say, that both are needed for explanations. And: Quantums are blurred either in space or velocity (Heisenberg). Blurring requires a continuum, i guess. Must be. I hope for a continuum too, because I tend towards panentheism, meaning, if God´s realm is continuous, ours is too, as both overlap, otherwise it would be hard to achieve a connection with God, like it is e.g. said to be so by Gnosticism. So I believe in continuum, though I am not sure, exactly which of Peirce´s methods of fixating belief have fixated mine.

 

Best, Helmut

 
 

Gesendet: Dienstag, 13. Februar 2024 um 19:58 Uhr
Von: "Jon Alan Schmidt" 
An: "Peirce-L" 
Betreff: Re: [PEIRCE-L] The Proper Way in Logic (was Peirce's Ongoing Semiotic Project)



Helmut, List:
 

According to Peirce, we discover (not invent) continuity in phaneroscopy--our conception of it comes from directly observing the flow of time, which he calls "the continuum par excellence, through the spectacles of which we envisage every other continuum" (CP 6.86, 1898), so that "to say it is continuous is just like saying that the atomic weight of oxygen is 16, meaning that that shall be the standard for all other atomic weights. The one asserts no more of Time than the other asserts concerning the atomic weight of oxygen; that is, just nothing at all" (CP 4.642, 1908). Here are a few more quotations about this.

 




CSP: To imagine time, time is required. Hence, if we do not directly perceive the flow of time, we cannot imagine time. Yet the sense of time is something forced upon common-sense. So that, if common-sense denies that the flow [of] time is directly perceived, it is hopelessly entangled in contradictions and cannot be identified with any distinct and intelligible conception. But to me it seems clear that our natural common-sense belief is that the flow of time is directly perceived. (NEM 3:60, c. 1895)

 
CSP: That this element [continuity] is found in experience is shown by the fact that all experience involves time. Now the flow of time is conceived as continuous. No matter whether this continuity is a datum of sense, or a quasi-hypothesis imported by the mind into experience, or even an illusion; in any case it remains a direct experience. (CP 7.535, 1899)


CSP: One opinion which has been put forward and which seems, at any rate, to be tenable and to harmonize with the modern logico-mathematical conceptions, is that our image of the flow of events receives, in a strictly continuous time, strictly continual accessions on the side of the future, while fading in a gradual manner on the side of the past, and that thus the absolutely immediate present is gradually transformed by an immediately given change into a continuum of the reality of which we are thus assured. The argument is that in this way, and apparently in this way only, our having the idea of a true continuum can be accounted for. (CP 8.123n, c. 1902)



 

Although Peirce acknowledges in the second passage that our direct perception/experience of time might be an illusion, he nevertheless suggests in the other two that its inescapability assures us of its reality, and that this is the only way to account for our having the idea of a true continuum at all. Moreover, right before the statement that I quoted at the end of my last post, he makes the case at greater length that we could not even imagine true continuity unless there were something in reality that corresponds to it.

 




CSP: I will submit for your consideration the following metaphysical principle which is of the nature of a retroduction: Whatever unanalyzable element sui generis seems to be in nature, although it be not really where it seems to be, yet must really be [in] nature somewhere, since nothing else could have produced even the false appearance of such an element sui generis. ...

In the same way, the very fact that there seems to be 3ns in the world, even though it be not where it seems to be, proves that real 3ns there must somewhere be. If the continuity of our inward and outward sense be not real, still it proves that continuity there really is, for how else should sense have the power of creating it?

Some people say that the sense of time is not in truth continuous, that we only imagine it to be so. If that be so, it strengthens my argument immensely. For how should the mind of every rustic and of every brute find it simpler to imagine time as continuous, in the very teeth of the appearances,--to connect it with by far the most difficult of all the conceptions which philosophers have ever thought out,--unless there were something in their real being which endowed such an idea 

Re: [PEIRCE-L] The Proper Way in Logic (was Peirce's Ongoing Semiotic Project)

[John F Sowa]

Jon,

Peirce's observations about the human perception of time as a continuum is 
important.  But there are many different ways of talking and thinking about 
time.   And there are also many different mathematical ways of formulating 
theories.  See my previous note in response to Edwina.

For starters, see the Wikipedia article about Whorf:  
https://en.wikipedia.org/wiki/Benjamin_Lee_Whorf .

The IndoEuropean way of thinking about time is by no means universal, and the 
long-standing puzzle by Zeno shows that the answer by Aristotle is not obvious. 
 It's not true that all people everywhere have the same ways of thinking about 
time, continuity, or the relation between time and continuity.

And the Peirce-Aristotle theory about the continuum is not the one that Cantor 
formalized.  More mathematicians today follow Cantor than Peirce.

JAS> he nevertheless suggests in the other two that its inescapability assures 
us of its reality, and that this is the only way to account for our having the 
idea of a true continuum

I admit that this statement is consistent with Peirce's quotations.  But the 
languages Peirce knew, although remarkably extensive among 19th century 
philosophers, do not exhaust the full range of thought about time or continuity 
or the relations between them.  And the different theories about continuity 
among professional mathematicians does not imply that the way people talk about 
time implies the way they must formulate theories about continuity.

The best we can say is that Peirce's views are consistent with views in SAE 
(Whorf's abbreviation for Standard Average European), but they are by no means 
universal.  They do not rule out other reasonable human ways of thinking about, 
talking about, and representing time and continuity.

John
_

From: "Jon Alan Schmidt" 

Helmut, List:

According to Peirce, we discover (not invent) continuity in phaneroscopy--our 
conception of it comes from directly observing the flow of time, which he calls 
"the continuum par excellence, through the spectacles of which we envisage 
every other continuum" (CP 6.86, 1898), so that "to say it is continuous is 
just like saying that the atomic weight of oxygen is 16, meaning that that 
shall be the standard for all other atomic weights. The one asserts no more of 
Time than the other asserts concerning the atomic weight of oxygen; that is, 
just nothing at all" (CP 4.642, 1908). Here are a few more quotations about 
this.

CSP: To imagine time, time is required. Hence, if we do not directly perceive 
the flow of time, we cannot imagine time. Yet the sense of time is something 
forced upon common-sense. So that, if common-sense denies that the flow [of] 
time is directly perceived, it is hopelessly entangled in contradictions and 
cannot be identified with any distinct and intelligible conception. But to me 
it seems clear that our natural common-sense belief is that the flow of time is 
directly perceived. (NEM 3:60, c. 1895)

CSP: That this element [continuity] is found in experience is shown by the fact 
that all experience involves time. Now the flow of time is conceived as 
continuous. No matter whether this continuity is a datum of sense, or a 
quasi-hypothesis imported by the mind into experience, or even an illusion; in 
any case it remains a direct experience. (CP 7.535, 1899)

CSP: One opinion which has been put forward and which seems, at any rate, to be 
tenable and to harmonize with the modern logico-mathematical conceptions, is 
that our image of the flow of events receives, in a strictly continuous time, 
strictly continual accessions on the side of the future, while fading in a 
gradual manner on the side of the past, and that thus the absolutely immediate 
present is gradually transformed by an immediately given change into a 
continuum of the reality of which we are thus assured. The argument is that in 
this way, and apparently in this way only, our having the idea of a true 
continuum can be accounted for. (CP 8.123n, c. 1902)

Although Peirce acknowledges in the second passage that our direct 
perception/experience of time might be an illusion, he nevertheless suggests in 
the other two that its inescapability assures us of its reality, and that this 
is the only way to account for our having the idea of a true continuum at all. 
Moreover, right before the statement that I quoted at the end of my last post, 
he makes the case at greater length that we could not even imagine true 
continuity unless there were something in reality that corresponds to it.

CSP: I will submit for your consideration the following metaphysical principle 
which is of the nature of a retroduction: Whatever unanalyzable element sui 
generis seems to be in nature, although it be not really where it seems to be, 
yet must really be [in] nature somewhere, since nothing else could have 
produced even the false appearance of such an element sui generis. ...
In the same way,

Re: [PEIRCE-L] Entropy and the Universal Categories (was Re: The Proper Way in Logic)

[Mike Bergman]

Hi John,

CSP: "Some of the ideas of prominent Thirdness which require closer 
study, preliminary to philosophy, are Continuity, Diffusion, Growth, and 
Intelligence. . . . the idea of an endless row of discrete objects, 
which is the image of the system of whole numbers, contains the idea of 
Thirdness in considerable prominence." (NEM 4.310, 1893-5)


I do not see intentionality in either diffusion or the whole numbers. 
BTW, an electronic search of Peirce's texts quickly turn up multiples of 
such examples.


I think I understand a point you are trying to make, but I think you 
could present it more correctly.


I'll leave the last comment to you as I am finished with this topic.

Best, Mike

On 2/13/2024 1:50 PM, John F Sowa wrote:

Mike,

I realize that Peirce mentioned "crystals and bees" in the same 
sentence.  But we have to consider his classification of the sciences. 
 Pure mathematics comes first, and it does not depend on anything 
else.  It incudes all varieties, including formal or mathematical 
logic, discrete math, and continuous math.  And Peirce followed 
Aristotle in insisting that continuous spaces (of which a line is a 
1-D space) do not have points as parts.  For Aristotle and Peirce, 
points are markers that designate a locus *ON *a space, but are not 
parts *OF* the space.


That is the basis for Aristotle's solution to Zeno's paradox about 
Achilles and the turtle, which Peirce knew very well.


Phaneroscopy depends only on mathematics, not semeiotic.  For Peirce, 
the phaneron is raw, unprocessed and uninterpreted experience. 
 (Modern cognitive science has more to say about these issues, but it 
may be deferred for analyzing what Peirce wrote.)  The result of 
analyzing the phaneron is expressed in linguistic terms, which depend 
on psychic science, which may employ the methods of any and every 
science that precedes it.  That includes all previous sciences, 
including the physical sciences and other psychic sciences.


MB> I categorically disagree. Intentionality may be an example of 
Thirdness, but is not definitive of it.


I agree that Peirce did not define 3ns in terms of intentionality. 
 But every example that he cited does indeed involve intentionality. 
 Can anybody find a single example of Thirdness in any writings by 
Peirce that does not involve intentions at least at the level of a 
bacterium swimming upstream in a glucose gradient.  Even a description 
of how plants grow would involve Thirdness in the same sense as a 
bacterium.


But a description of a crystal could be stated in two ways.  If you 
consider the structure of the crystal as the desired final state, then 
a description in those terms would be stated in *TERMINOLOGICAL 
*thirdness.  That may be the reason why Peirce wrote "crystals and 
bees".   And that answer involves something very close to 
intentionality:  In forming a diamond, each atom of carbon goes to a 
position where it minimizes the total energy of the crystal structure. 
 In effect, the carbon atom "wants" to minimize energy in the same 
sense that a bacterium wants to ingest glucose.


But if you look at the way crystals actually grow in nature, each atom 
or molecule in the crystal goes into its spot in the structure by 
principles of 2-ness -- following the strongest forces that act upon 
it.  Those are *EXTERNAL *forces that act upon the atoms.  That is 
very different from the *INTERNAL *forces in the bacterium that govern 
how it behaves in the presence of an external glucose gradient.


Take for example the two most common carbon crystals:  graphite and 
diamond.  At modest level of heat, such as burning wood or paper, any 
unburnt carbon forms soot.  If you examine that soot with a powerful 
microscope, you'll find that the soot particles contain very small 
graphite crystals mixed with other residues of burning.  That can be 
explained by the atoms clumping together in a low energy state by 2ns, 
not 3ns,


But if you put the graphite under high compression at high 
temperatures, you can force the carbon atoms even closer together in a 
state with lower energy:  diamond crystals. Those are also external 
forces that act upon the carbon atoms.


Peirce knew the chemistry of his day very well.  But the atomic 
hypothesis of his day and theories about crystal formation were in 
their infancy.  With modern theories, descriptions at the level of 2ns 
can explain chemical reactions and the way atoms move in forming crystals.

John


*From*: "Mike Bergman" 
*Sent*: 2/12/24 5:19 PM

Hi John,

I categorically disagree. Intentionality may be an example of 
Thirdness, but is not definitive of it. JAS just posted "Continuity 
represents 3ns almost to perfection" (CP 1.337, c. 1882), which I 
concur best captures (with Mind) Peirce's prominent view of Thirdness, 
and contintuity does not require intentionality. You might even 
diagram it out.


And don't forget crystals (a

Re: [PEIRCE-L] Entropy and the Universal Categories (was Re: The Proper Way in Logic)

[Jon Alan Schmidt]

Mike, List:

Indeed, the online Commens Dictionary entry for 3ns (
http://www.commens.org/dictionary/term/thirdness) consists of 21 Peirce
quotations, none of which includes the word "intentionality." Two of them
do have the word "intention," and here is the first.

CSP: Nature herself often supplies the place of the intention of a rational
agent in making a 3ns genuine and not merely accidental; as when a spark,
as third, falling into a barrel of gunpowder, as first, causes an
explosion, as second. But how does nature do this? By virtue of an
intelligible law according to which she acts. If two forces are combined
according to the parallelogram of forces, their resultant is a real 3rd.
Yet any force may, by the parallelogram of forces, be mathematically
resolved into the sum of two others, in an infinity of different ways. Such
components, however, are mere creations of the mind. What is the
difference? As far as one isolated event goes, there is none; the real
forces are no more present in the resultant than any components that the
mathematician may imagine. But what makes the real forces really there is
the general law of nature which calls for them, and not for any other
components of the resultant. Thus, intelligibility, or reason objectified,
is what makes 3ns genuine. (CP 1.366, EP 1:255, 1886-7)


In this excerpt, it is *intelligibility *that is essential for genuine 3ns,
not intentionality; at least, not "the intention of a rational agent."
Anything that occurs "by virtue of an intelligible law"-- including a spark
causing gunpower to explode, as well as (presumably) graphite crystals
forming in soot or those same crystals becoming diamonds under high
pressure and temperature--is an example of 3ns. Peirce says much the same
thing many years later.

CSP: The third element of the phenomenon is that we perceive it to be
intelligible, that is, to be subject to law, or capable of being
represented by a general sign or Symbol. But I say the same element is in
all signs. The essential thing is that it is capable of being represented.
Whatever is capable of being represented is itself of a representative
nature. (CP 8.268, 1903)


As I noted earlier in this thread (quoting that last sentence), for Peirce,
although "*really being* and *being represented* are very different" (EP
2:303, c. 1901), really being and being representable--and thus being of
the nature of a sign--are the same. "The very entelechy of being lies in
being representable. ... This appears mystical and mysterious simply
because we insist on remaining blind to what is plain, that there can be no
reality which has not the life of a symbol" (EP 2:324, c. 1901). After all
...

CSP: [T]he Universe is a vast representamen, a great symbol of God's
purpose, working out its conclusions in living realities. Now every symbol
must have, organically attached to it, its Indices of Reactions and its
Icons of Qualities; and such part as these reactions and these qualities
play in an argument, that they of course play in the Universe, that
Universe being precisely an argument" (CP 5.119, EP 2:193-194, 1903).

CSP: [T]he explanation of the phenomenon lies in the fact that the entire
universe,--not merely the universe of existents, but all that wider
universe, embracing the universe of existents as a part, the universe which
we are all accustomed to refer to as "the truth,"--that all this universe
is perfused with signs, if it is not composed exclusively of signs. (CP
5.448n, EP 2:394, 1906)


Here is the second quotation for 3ns with the word "intention."

CSP: Let us now take up being *in futuro*. As in the other cases, this is
merely an avenue leading to a purer apprehension of the element it
contains. An absolutely pure conception of a Category is out of the
question. Being *in futuro* appears in mental forms, intentions and
expectations. Memory supplies us a knowledge of the past by a sort of brute
force, a quite binary action, without any reasoning. But all our knowledge
of the future is obtained through the medium of something else. ...
Intellectual triplicity, or Mediation, is my third category. (CP 2.86, 1902)


In this excerpt, the emphasis is ultimately on *mediation*, which is what
Peirce describes elsewhere as the purest conception of 3ns one can have (CP
1.530, 1903). However, the ellipsis omits a considerable amount of text,
including a few examples where intention is indeed the hallmark of 3ns--a
dog fetching a book for its master, a man giving a brooch to his wife, and
a merchant throwing a datestone that hits a Jinee. The absence of intention *in
these specific cases* would render them "purely mechanical actions," dyadic
instead of triadic, 2ns rather than 3ns. Nevertheless, as already noted,
there are abundant passages (like the first quotation above) where Peirce
treats other ideas, where intentionality is lacking, as paradigmatic of
3ns--such as continuity, diffusion, the whole numbers, and even explosions.

Regards,

Jon Alan Schmidt 

Re: [PEIRCE-L] The Proper Way in Logic (was Peirce's Ongoing Semiotic Project)

[Edwina Taborsky]

John, list

I’m not a fan of the Whorf-Sapir sociolinguistics hypotheses…Objective reality 
exists, regardless of how we talk about it - and I maintain that its influence 
can be far stronger than words ie - Secondness has its own way of intruding on 
our words. And mathematics has nothing to do with sociolinguistic relativism.

As for time - I tend to follow Matsuno’s analysis [Koichiro Matsuno] with his 
three types of time: present, perfect and progressive, which can be compared 
with Peircean 1ns, 2ns and 3ns. …and Peirce has written about the temporal and 
spatial nature of these three categories extensively [ ie, no need for 
quotations].

Yes, 3ns includes continuity -of its habits - but, I don’t see this type of 
continuity as the same as the continuous semiosic functions of the universe.  
Imagine what our universe would be, if it stopped transforming x into y via its 
mediative  process?….But, a habit in 3ns can and does change…

Edwina

> On Feb 13, 2024, at 4:40 PM, John F Sowa  wrote:
> 
> Jon,
> 
> Peirce's observations about the human perception of time as a continuum is 
> important.  But there are many different ways of talking and thinking about 
> time.   And there are also many different mathematical ways of formulating 
> theories.  See my previous note in response to Edwina.
> 
> For starters, see the Wikipedia article about Whorf:  
> https://en.wikipedia.org/wiki/Benjamin_Lee_Whorf .
> 
> The IndoEuropean way of thinking about time is by no means universal, and the 
> long-standing puzzle by Zeno shows that the answer by Aristotle is not 
> obvious.  It's not true that all people everywhere have the same ways of 
> thinking about time, continuity, or the relation between time and continuity.
> 
> And the Peirce-Aristotle theory about the continuum is not the one that 
> Cantor formalized.  More mathematicians today follow Cantor than Peirce.
> 
> JAS> he nevertheless suggests in the other two that its inescapability 
> assures us of its reality, and that this is the only way to account for our 
> having the idea of a true continuum 
> 
> I admit that this statement is consistent with Peirce's quotations.  But the 
> languages Peirce knew, although remarkably extensive among 19th century 
> philosophers, do not exhaust the full range of thought about time or 
> continuity or the relations between them.  And the different theories about 
> continuity among professional mathematicians does not imply that the way 
> people talk about time implies the way they must formulate theories about 
> continuity.
> 
> The best we can say is that Peirce's views are consistent with views in SAE 
> (Whorf's abbreviation for Standard Average European), but they are by no 
> means universal.  They do not rule out other reasonable human ways of 
> thinking about, talking about, and representing time and continuity.
> 
> John
> _
>  
> From: "Jon Alan Schmidt" 
> 
> Helmut, List:
> 
> According to Peirce, we discover (not invent) continuity in phaneroscopy--our 
> conception of it comes from directly observing the flow of time, which he 
> calls "the continuum par excellence, through the spectacles of which we 
> envisage every other continuum" (CP 6.86, 1898), so that "to say it is 
> continuous is just like saying that the atomic weight of oxygen is 16, 
> meaning that that shall be the standard for all other atomic weights. The one 
> asserts no more of Time than the other asserts concerning the atomic weight 
> of oxygen; that is, just nothing at all" (CP 4.642, 1908). Here are a few 
> more quotations about this.
> 
> CSP: To imagine time, time is required. Hence, if we do not directly perceive 
> the flow of time, we cannot imagine time. Yet the sense of time is something 
> forced upon common-sense. So that, if common-sense denies that the flow [of] 
> time is directly perceived, it is hopelessly entangled in contradictions and 
> cannot be identified with any distinct and intelligible conception. But to me 
> it seems clear that our natural common-sense belief is that the flow of time 
> is directly perceived. (NEM 3:60, c. 1895)
> 
> CSP: That this element [continuity] is found in experience is shown by the 
> fact that all experience involves time. Now the flow of time is conceived as 
> continuous. No matter whether this continuity is a datum of sense, or a 
> quasi-hypothesis imported by the mind into experience, or even an illusion; 
> in any case it remains a direct experience. (CP 7.535, 1899)
> 
> CSP: One opinion which has been put forward and which seems, at any rate, to 
> be tenable and to harmonize with the modern logico-mathematical conceptions, 
> is that our image of the flow of events receives, in a strictly continuous 
> time, strictly continual accessions on the side of the future, while fading 
> in a gradual manner on the side of the past, and that thus the absolutely 
> immediate present is gradually transformed by an immediately 

Re: [PEIRCE-L] Entropy and the Universal Categories (was Re: The Proper Way in Logic)

[Edwina Taborsky]

John, list

I think it would help if you defined ‘intentionality’.   Is it involved in all 
human actions? Did the bus driver intentionally run over the pedestrian? 

Edwina

> On Feb 13, 2024, at 3:26 PM, John F Sowa  wrote:
> 
> Edwina,
> 
> Please see my response to Mike.
> 
> I used the word 'intentionality' because it (or something like it) is 
> involved in all human actions.  For example, I can intentionally walk to the 
> store.  But what about each step in the walk?  In effect, it is intentional, 
> but it's only conscious when there is a puddle or a broken place in the 
> sidewalk.
> 
> Other animals at every level and even plants act upon principles that would 
> be called intentional if they had been human.  But consciousness is not 
> necessary.  And even for humans, all actions appear to have the some kind of 
> intentionality, but the actors themselves will often say that they did it 
> "absent mindedly".
> 
> But absent minded actions are often done when people are "multitasking", such 
> as talking on their cell phones while crossing the street and getting run 
> over by a bus.  They didn't intend to get run over by the bus, but they did 
> intend to cross the street.  The steps of walking were not conscious, but 
> they were necessary parts of an intentional process.
> 
> In effect, Thirdness is involved in every intentional action.  And every 
> instance of Thirdness by any living being could be called intentional if a 
> human did it.   Can anybody find an example of Thirdness in any of Peirce's 
> writings that could not be considered intentional if it had been performed by 
> a human?
> 
> John
>  
> 
> From: "Edwina Taborsky" 
> 
> List
> 
> I agree with Mike. Thirdness, in my view, does not imply or require 
> intentionality. That, after all, suggests some kind of consciousness - and I 
> think we find Thirdness in chemical and physical matter - and these forms of 
> matter do not include consciousness.
> 
> I have a problem with the quote of “Continuity presents 3ns almost to 
> perfection’ 1.337. I think that the rules of Thirdness CAN and must be, for a 
> certain period of time, ‘continuous and stable.After all- we cannot live iin 
> a world where a cat suddenly transforms into a dog.  BUT, since thirdness 
> also includes 2ns and 1ns, then, it contains within itself, the ability to 
> interact with other units of matter - as well as chance - and thus, has the 
> capacity to accept more data and thus, change these ‘continuous rules’ and 
> so, adapt and evolve.
> 
> Again - I consider that Peircean ‘continuity’ is not 3ns but is the 
> continuous morphological semiosis formation of energy-into-matter - which is 
> ongoing [ or else, as has been pointed out, entropy sneaks in]….
> 
> Edwina
> _ _ _ _ _ _ _ _ _ _
> ARISBE: THE PEIRCE GATEWAY is now at 
> https://cspeirce.com  and, just as well, at 
> https://www.cspeirce.com .  It'll take a while to repair / update all the 
> links!
> ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON 
> PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu 
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> co-managed by him and Ben Udell.

_ _ _ _ _ _ _ _ _ _
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https://www.cspeirce.com .  It'll take a while to repair / update all the links!
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON 
PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . 
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► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;  and 
co-managed by him and Ben Udell.

Re: [PEIRCE-L] The Proper Way in Logic (was Peirce's Ongoing Semiotic Project)

[Gary Richmond]

John, List,

JFS: More mathematicians today follow Cantor than Peirce.

And not only today but in Peirce's day as well. Peirce referred to
Cantor's  conception as a "pseudo-continuum," a "bottoms-up" approach. It's
too bad that a contemporary mathematician hasn't written a paper explaining
the virtues of Peirce's top-down approach. Of course on List and in his
*Transactions* paper, "Peirce's Topical Continuum," Jon Alan Schmidt has
argued for Peirce's alternative "top-down" conception. In light of the
current discussion, I reread JAS's paper and can heartily recommend it to
anyone wishing to understand the "top-down" vs "bottom-up" distinction. See:

Peirce's Topical Continuum: A “Thicker” Theory

Jon Alan Schmidt 

*Transactions of the Charles S. Peirce Society
* 56 (1):62-80 (2020)   Copy   B
IBTEX
Abstract
Although Peirce frequently insisted that continuity was a core component of
his philosophical thought, his conception of it evolved considerably during
his lifetime, culminating in a theory grounded primarily in topical
geometry. Two manuscripts, one of which has never before been published,
reveal that his formulation of this approach was both earlier and more
thorough than most scholars seem to have realized. Combining these and
other relevant texts with the better-known passages highlights a key
ontological distinction: a collection is bottom-up, such that the parts are
real and the whole is an ens rationis, while a continuum is top-down, such
that the whole is real and the parts are entia rationis. Accordingly, five
properties are jointly necessary and sufficient for Peirce’s topical
continuum: rationality, divisibility, homogeneity, contiguity, and
inexhaustibility.

I'd also like to take this opportunity to join those on the list who
question your insistence that 3ns = intentionality. I haven't anything to
add to what Edwina, Mike, and now Jon has written except to note that even
Tom Short in his book on Peire's semeiotic goes no further than to say that
"the intentionality of thought is a special case of significance" which
hardly equates it with intentionality.

Best,

Gary Richmond





On Tue, Feb 13, 2024 at 4:40 PM John F Sowa  wrote:

> Jon,
>
> Peirce's observations about the human perception of time as a continuum is
> important.  But there are many different ways of talking and thinking about
> time.   And there are also many different mathematical ways of formulating
> theories.  See my previous note in response to Edwina.
>
> For starters, see the Wikipedia article about Whorf:
> https://en.wikipedia.org/wiki/Benjamin_Lee_Whorf .
>
> The IndoEuropean way of thinking about time is by no means universal, and
> the long-standing puzzle by Zeno shows that the answer by Aristotle is not
> obvious.  It's not true that all people everywhere have the same ways of
> thinking about time, continuity, or the relation between time and
> continuity.
>
> And the Peirce-Aristotle theory about the continuum is not the one that
> Cantor formalized.  More mathematicians today follow Cantor than Peirce.
>
> JAS> he nevertheless suggests in the other two that its inescapability
> assures us of its reality, and that this is the only way to account for our
> having the idea of a true continuum
>
> I admit that this statement is consistent with Peirce's quotations.  But
> the languages Peirce knew, although remarkably extensive among 19th century
> philosophers, do not exhaust the full range of thought about time or
> continuity or the relations between them.  And the different theories about
> continuity among professional mathematicians does not imply that the way
> people talk about time implies the way they must formulate theories about
> continuity.
>
> The best we can say is that Peirce's views are consistent with views in
> SAE (Whorf's abbreviation for Standard Average European), but they are by
> no means universal.  They do not rule out other reasonable human ways of
> thinking about, talking about, and representing time and continuity.
>
> John
> _
>
> *From*: "Jon Alan Schmidt" 
>
> Helmut, List:
>
> According to Peirce, we discover (not invent) continuity in
> phaneroscopy--our conception of it comes from directly observing the flow
> of time, which he calls "the continuum *par excellence*, through the
> spectacles of which we envisage every other continuum" (CP 6.86, 1898), so
> that "to say it is continuous is just like saying that the atomic weight of
> oxygen is 16, meaning that that shall be the standard for all other atomic
> weights. The one asserts no more of Time than the other asserts concerning
> the atomic weight of oxygen; that is, just nothing at all" (CP 4.642,
> 1908). Here are a few more quotations about this.
>
> CSP: To imagine time, ti

Re: [PEIRCE-L] The Proper Way in Logic (was Peirce's Ongoing Semiotic Project)

[Gary Richmond]

Erratum: I meant to write at the end of my post "Tom Short in his book on
Peire's semeiotic goes no further than to say that "the intentionality of
thought is a special case of significance" which hardly equates it with
3ns" (not "intentionality," of course). GR

On Tue, Feb 13, 2024 at 7:31 PM Gary Richmond 
wrote:

> John, List,
>
> JFS: More mathematicians today follow Cantor than Peirce.
>
> And not only today but in Peirce's day as well. Peirce referred to
> Cantor's  conception as a "pseudo-continuum," a "bottoms-up" approach. It's
> too bad that a contemporary mathematician hasn't written a paper explaining
> the virtues of Peirce's top-down approach. Of course on List and in his
> *Transactions* paper, "Peirce's Topical Continuum," Jon Alan Schmidt has
> argued for Peirce's alternative "top-down" conception. In light of the
> current discussion, I reread JAS's paper and can heartily recommend it to
> anyone wishing to understand the "top-down" vs "bottom-up" distinction. See:
>
> Peirce's Topical Continuum: A “Thicker” Theory
> 
> Jon Alan Schmidt 
>
> *Transactions of the Charles S. Peirce Society
> * 56 (1):62-80 (2020)   Copy
>  BIBTEX
> Abstract
> Although Peirce frequently insisted that continuity was a core component
> of his philosophical thought, his conception of it evolved considerably
> during his lifetime, culminating in a theory grounded primarily in topical
> geometry. Two manuscripts, one of which has never before been published,
> reveal that his formulation of this approach was both earlier and more
> thorough than most scholars seem to have realized. Combining these and
> other relevant texts with the better-known passages highlights a key
> ontological distinction: a collection is bottom-up, such that the parts are
> real and the whole is an ens rationis, while a continuum is top-down, such
> that the whole is real and the parts are entia rationis. Accordingly, five
> properties are jointly necessary and sufficient for Peirce’s topical
> continuum: rationality, divisibility, homogeneity, contiguity, and
> inexhaustibility.
>
> I'd also like to take this opportunity to join those on the list who
> question your insistence that 3ns = intentionality. I haven't anything to
> add to what Edwina, Mike, and now Jon has written except to note that even
> Tom Short in his book on Peire's semeiotic goes no further than to say that
> "the intentionality of thought is a special case of significance" which
> hardly equates it with intentionality.
>
> Best,
>
> Gary Richmond
>
>
>
>
>
> On Tue, Feb 13, 2024 at 4:40 PM John F Sowa  wrote:
>
>> Jon,
>>
>> Peirce's observations about the human perception of time as a continuum
>> is important.  But there are many different ways of talking and thinking
>> about time.   And there are also many different mathematical ways of
>> formulating theories.  See my previous note in response to Edwina.
>>
>> For starters, see the Wikipedia article about Whorf:
>> https://en.wikipedia.org/wiki/Benjamin_Lee_Whorf .
>>
>> The IndoEuropean way of thinking about time is by no means universal, and
>> the long-standing puzzle by Zeno shows that the answer by Aristotle is not
>> obvious.  It's not true that all people everywhere have the same ways of
>> thinking about time, continuity, or the relation between time and
>> continuity.
>>
>> And the Peirce-Aristotle theory about the continuum is not the one that
>> Cantor formalized.  More mathematicians today follow Cantor than Peirce.
>>
>> JAS> he nevertheless suggests in the other two that its inescapability
>> assures us of its reality, and that this is the only way to account for our
>> having the idea of a true continuum
>>
>> I admit that this statement is consistent with Peirce's quotations.  But
>> the languages Peirce knew, although remarkably extensive among 19th century
>> philosophers, do not exhaust the full range of thought about time or
>> continuity or the relations between them.  And the different theories about
>> continuity among professional mathematicians does not imply that the way
>> people talk about time implies the way they must formulate theories about
>> continuity.
>>
>> The best we can say is that Peirce's views are consistent with views in
>> SAE (Whorf's abbreviation for Standard Average European), but they are by
>> no means universal.  They do not rule out other reasonable human ways of
>> thinking about, talking about, and representing time and continuity.
>>
>> John
>> _
>>
>> *From*: "Jon Alan Schmidt" 
>>
>> Helmut, List:
>>
>> According to Peirce, we discover (not invent) continuity in
>> phaneroscopy--our conception of it comes from directly observing the flow
>> of time, which he calls "the continuum *par excellence*, through the
>> spec

[PEIRCE-L] Who, What, When, Where, How, and Why (was Sign Relations

[John F Sowa]

Jon,

I completely agree with the following principle:

JA> Another aspect of a sign's complete meaning concerns the reference a sign 
has to its interpretants...

And there are six kinds of reference that a sign my have to its interpretants.  
Each kind corresponds to one of the six basic question words in English (or 
their equivalents in other languages).  Questions that begin with the first 
four question words may be answers with one word or phrase:  Who, What, When, 
and Where.  Any such question may be answered with one word or phrase and a 
MONADIC relation.

Questions that begin with How can be answered in a sentence with a dyadic verb, 
a DYADIC relation.

And questions that begin with Why require require a sentence with a verb that 
requires a subject, object, and an indirect object or  a prepositional phrase:  
a TRIADIC relation.

In short, that is the distinction between Peirce's Firstness, Secondness, and 
Thirdness.  The monadic relations of Firstness express answers to the words 
Who, What, When, or Where,  The dyadic relations of Secondness express answers 
to the word How.  And the triadic relations of Thirdness answer questions to 
the word Why.

In summary. all examples of Thirdness are answers to Why-questions.  They all 
express some kind of intention or purpose or explanation or reason for the 
triadic connection.

John


From: "Jon Awbrey" 
Sent: 2/13/24 9:02 AMc

Another aspect of a sign's complete meaning concerns the reference
a sign has to its interpretants, which interpretants are collectively
known as the “connotation” of the sign. In the pragmatic theory of
sign relations, connotative references fall within the projection
of the sign relation on the plane spanned by its sign domain and
its interpretant domain.

In the full theory of sign relations the connotative aspect of meaning
includes the links a sign has to affects, concepts, ideas, impressions,
intentions, and the whole realm of an interpretive agent's mental states
and allied activities, broadly encompassing intellectual associations,
emotional impressions, motivational impulses, and real conduct.

Taken at the full, in the natural setting of semiotic phenomena, this
complex system of references is unlikely ever to find itself mapped in
much detail, much less completely formalized, but the tangible warp of
its accumulated mass is commonly alluded to as the connotative import
of language.

Formally speaking, however, the connotative aspect of meaning presents
no additional difficulty. The dyadic relation making up the connotative
aspect of a sign relation L is notated as Con(L). Information about the
connotative aspect of meaning is obtained from L by taking its projection
on the sign‑interpretant plane. We may visualize this as the “shadow” L
casts on the 2‑dimensional space whose axes are the sign domain S and the
interpretant domain I. The connotative component of a sign relation L,
alternatively written in any of forms, proj_{SI} L, L_SI, proj₂₃ L, and
L₂₃, is defined as follows.

• Con(L) = proj_{SI} L = {(s, i) ∈ S × I : (o, s, i) ∈ L for some o ∈ O}.

Tables 4a and 4b show the connotative components of the sign relations
associated with the interpreters A and B, respectively. The rows of
each Table list the ordered pairs (s, i) in the corresponding projections,
Con(L_A), Con(L_B) ⊆ S × I.

Tables 4a and 4b. Connotative Components Con(L_A) and Con(L_B)
• 
https://inquiryintoinquiry.files.wordpress.com/2020/06/sign-relation-twin-tables-con-la-con-lb.png

Resources —

Sign Relations
• https://oeis.org/wiki/Sign_relation

Connotation
• https://oeis.org/wiki/Sign_relation#Connotation

Document History
• https://oeis.org/wiki/Sign_relation#Document_history

Regards,

Jon

cc: https://www.academia.edu/community/LmnnXP
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